Environmental Modeling
Steven I. Gordon
Ohio Supercomputer Center
sgordon@osc.edu
June, 2004
Environmental Models Offer Many Options
• Many models
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–
–
–
–
Atmospheric processes
Hydrologic processes
Ecological systems
Natural hazards
Many interactions
• Many scales
– Local habitats
– Regional – mesoscale
– Global
Problems in Instruction
• Modeling complex, dynamic systems
• Changes occur both spatially and temporally
• Quality of data to confirm model validity often
questionable
• High degrees of uncertainty
• Many different processes cross disciplinary boundaries
– Challenge for students with varying background
– Challenge for faculty trying to apply to instruction
Mixed Approaches
• Models based on physical theory
– Fluid dynamics
– Mechanics
– Biochemistry
• Models based on statistical and empirical
estimates
– Used to simplify the complex dynamic systems
– Based on abstractions that do not always apply
Many Places Many Parameters
• Requirements for data describing initial conditions at each
place in the model
– Amount of data required dependent on model scale
– Data acquisition difficult
– Increasing availability of spatial data from public sources
• Most models embed many parameter choices
– Values found under different circumstances
– Calculated based on different principles
• Choices can make model use decisions dizzying
Basic Model Components
• State variables describing status as different places
at time zero
• Flow over time and space of matter, energy,
organisms
• Transformation of physical, chemical, or
biological characteristics over time
Alternative Representations
• What governs the movement from one place to
another?
• How does movement vary with changes in
environmental conditions? How is this change
represented (steady steady, stochastically,
statistically)?
• How will space be represented – implicitly, one,
two or three dimensions?
First Example – Dissolved Oxygen in a Stream
• Measure of health – ability to support diverse
ecosystem
• Basic relationship
– Inversely related to temperature
– Range between 0 and 14 ppm (mg/l)
Conceptual model
• Organic waste (BOD) decomposed by
bacteria that use oxygen
– DO=f(1/BOD)
• Two processes
– Deoxygenation
– Reaeration
Graphical Representation of Point
Discharge and DO
1:
Dissolv ed Oxy gen: 1 8
DOSaturation
1
1
1
1:
6
1
1:
Page 1
4
0.00
6.25
12.50
Day s
Dissolv ed Oxy gen of Sugar Creek
18.75
25.00
10:09 AM Sun, Apr 11, 2004
Basic Equations
dDt
 k 1 L  k 2 Dt  1
dt
• Where D = dissolved oxygen deficit over time
• L = concentration of organic matter requiring
decomposition
• k1= coefficient of deoxygenation
• k2 = coefficient of reaeration
Stella Model Example
Excel Engineering Version
• Qual2K
• Based on EPA code for DO called Qual2E
• http://www.epa.gov/athens/wwqtsc/html/qual2
k.html
• Example run
Complexity of the Model
• Choose which aspects to focus on
• Leave the rest as a “black box”
• Create an exercise that focuses on variables
of interest
– E.G. BOD load; sensitivity to reaeration parameter
and temperature
Simple Point Source/Receptor Model
Simple Point Source/Receptor Model
Y
Z
X
Simple Point Source/Receptor Model
Virtual
Origin
h
H
h
Plume
Centerline
Gaussian Plume Model
• Dispersion in downwind direction proportional
to wind speed (x)
• Dispersion in y and z direction normally
distributed along the plume center line
• Mean concentration and dispersion vary with
stability class in known empirical quantity
Equation
2
 -y 


(z
H)
Q




C ( x, y, z ) 
exp 
exp
2 
2

2yz 
2 z 
 2 y 




2
Where:
C (x,y,z) = concentration of pollutant in 3 dimensions
given steady state emission
X = horizontal distance from source in direction of wind
vector and along plume centerline
Y= horizontal distance perpendicular to and measured
from the plume center line
Z= vertical distance from ground to plume center line
Q= mass rate of production of pollutant over time
Where:
Ū = mean wind speed in the x direction
H = effective height of plume


y
z
 standard deviation in cross - wind direction
 vertical standard deviation from PCL
Equation
2
 -y 


(z
H)
Q




C ( x, y, z ) 
exp 
exp
2 
2

2yz 
2 z 
 2 y 




2
Emission
dispersed as
statistical
dispersion in 3
directions
Dispersion in cross-wind
and vertical dimension
Empirically Solve for Coefficients
Solving the Equation
• Probability distribution of different wind
speed, direction, stability class occurrence
• Solve the model for each condition
• Weight the answer by the frequency of each
condition
Stability Wind Rose
Excel Version of the Model
The Climatological Dispersion Model
Alternative Approaches
• Find a simple version of a model to run in
Stella or a spreadsheet
• Have students add to the simple model by
taking advantage of the
documentation/discussion in more complex
models
• Run a more complex model but vary only a
few variables most relevant to the class topics
Create and Test a Set of Exercises
• Regardless of approach – need to carefully
prepare instructions that include:
–
–
–
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Readings on the model basis
Step-by-step instructions
Realistic scenarios
Clear list of expected exercise outcomes
Opportunities for feedback
Sources of Information
• See attached sheet with web links to a variety
of modeling and data sites